Question

A website randomly selects among 10 products to discount each day. The color printer of interest to you is discounted today. Determine the following:_______.
(a) What is the probability that this product is first discounted again exactly 10 days from now?
(b) What is the expected number of days until this product is again discounted?

Answer 1

Answer:

a) P = 0.039

b) The expected number of days is 10 days.

Step-by-step explanation:

The most appropiate distribution to use in this case is the geometric distribution, in order to calculate the probability of a success after k failure trials.

The probability of success, as each of the 10 products are assumed to have fair probabilities, is:

$p=1/10=0.1$

Then, the probability that our product is not selected any given day is:

$q=1-p=1-0.1=0.9$

a) The probability that exactly this product is selected exactly 10 days from now is the probability that is not selected (probbility q) for the next 9 days and selected (probability p) at the 10th day:

$P=q^9p^1=0.9^9\cdot0.1=0.3874\cdot0.1=0.039$

b) The expected number of days is calculated as:

$E(X)=\dfrac{1}{p}=\dfrac{1}{0.1}=10$